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Can we calculate the velocity of individual molecules by vector
addition of their motion when at rest and the overall motion of the object?
(Answer without reference to the uncertainty principle is prefered...)
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Hi Chris,

Yes, you can, indeed, use vector addition to calculate velocities. I'm not sure if I understood your question correctly but it seems that you wanted to know if you could calculate the motion of a molecule trapped in a moving box by just doing vector addition of the motion of the box to the motion of the molecule. As long as we're ignoring any quantum effects, we might as well make the further assumption that everything's non-relativistic.

That being the case, you have the situation of a classical particle trapped in a moving box. Further, the particle is moving relative to the box. If we confine it to the one-dimensional case, we can simply add their velocities (after defining one direction as the positive direction) to get the overall motion of the particle from the point of view of a stationary observer in a coordinate system in which both the box and the particle are in motion. If you want to deal in higher dimensions (e.g., 3-d), then you can simply do vector addition by breaking the velocity vector of each object (the box and the particle) into its components and add the components. Once this is done, just reconstruct the final vector from the resultant components.

Since you didn't mention a grade level, I assumed some familiarity with basic vector concepts and use. However, if all of the above seemed like some obscure Martian dialect, just mosey on over to the sites below to learn all about vectors and vector addition and subtraction (and multiplication, division, etc.).

Happy vectoring,

Rick.

- Vectors -- A great introduction
- Introduction to Vectors and Coordinate Systems -- A chapter from an introductory physics class
- Vectors, tensors, and matrices -- Definitely falls under advanced

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